Which of these is the standard form of the following function?
f(x) = -9(x + 5)2 + 4



f(x) = 9x2 − 90x − 221


f(x) = -9x2 − 90x − 221


f(x) = 9x2 − 180x + 221


f(x) = -9x2 − 180x − 221

The total charge for the rooms will be $197.55.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

The charge for one room = $21.95

Total number of rooms = 3+2+4=9 rooms

Total charges for the room= Charge for one room × total number of room

Substitute the values:-

The total charge for the room = 21.95 × 9 = 197.55

Hence, the total charge for the room is 197.55

The complete question is given below:-

Landon Elliot fumigates rooms and charges $21.95 per room. on Monday, he fumigated 3 rooms in one house, 2 in another, and 4 in a third. find his total charges.

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Answer:

Step-by-step explanation:

1. -(5/x^6)

2. 4398046511104

3. 65536

4. 1/100

5. 1/5764801

The correct description that defines the prism square is option B: "Is another hand instrument that is also used to determine or set out right angles."

A prism square is a tool used in construction and woodworking to establish or verify right angles. It consists of a triangular-shaped body with a 90-degree angle and two perpendicular sides. The edges of the prism square are straight and typically have measurement markings. It is commonly used in carpentry, masonry, and other trades where precise right angles are essential for accurate and square construction. Option A describes a different tool involving mirrors set at an angle, which is not related to the prism square. Option C refers to a different instrument used for measuring slopes and is not directly related to the prism square.

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The probability that a defective component can be detected by only one inspector is 0.2112. the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

(a) To calculate the probability that a defective component will be detected by only one inspector, we can use the formula for conditional probability: P(detected by first inspector | not detected by second inspector) = P(detected by first inspector and not detected by second inspector) / P(not detected by second inspector).

The probability that a defective component will be detected by the first inspector and not detected by the second inspector can be calculated as follows: P(detected by first inspector and not detected by second inspector) = P(detected by first inspector) * P(not detected by second inspector | detected by first inspector) = 0.88 * (1 - 0.88) = 0.1056.

The probability that a defective component will not be detected by the second inspector is: P(not detected by second inspector) = 1 - P(detected by second inspector) = 1 - 0.88 = 0.12.

The probability that a defective component will be detected by exactly one of the two inspectors can be calculated as follows: P(detected by exactly one inspector) = P(detected by first inspector and not detected by second inspector) + P(detected by second inspector and not detected by first inspector) = 0.1056 + 0.1056 = 0.2112.

(b) To calculate the probability that all three defective components in a batch escape detection by both inspectors, we can use the formula for independent events: P(all three defective components escape detection) = P(first defective component escapes detection) * P(second defective component escapes detection) * P(third defective component escapes detection) = (1 - 0.88)^3 = 0.00178.

So the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

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Complete question : components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 88% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 24% of all defective components. what is the probability that the following occur? (a) A defective component will be detected only by the first inspector? A defective component will be detected by exactly one of the two inspectors? (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

For the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

As given in the question,

Geometric mean GM = 30

Let us assume the first number is x

and second number i.e. 9 times of the first number is 9x

By the formula GM = \(\sqrt{x.y}\)

Now putting the value

30 = \(\sqrt{x.9x}\)

30 = \(\sqrt{9x^{2} }\)

30 = 3x (∴ square root of 9 is 3 and sq root of x² is x)

10 = x  (by dividing both the side by 3)

Therefore, for the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

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Answer:

x> 24/_7

x>_3.43

..............

Answer:

x=6

Step-by-step explanation:

Answer: 12.81 (look at the image for the explanation)

Step-by-step explanation:

To solve the given 1-dimensional heat equation problem, we can use the method of separation of variables. The problem is defined as follows:

Partial Differential Equation (PDE): ∂u/∂t = α^2 ∂^2u/∂x^2, for t > 0 and 0 < x < 5.

Boundary conditions:
1. u(0, t) = 0
2. u(5, t) = 0

Initial condition: u(x, 0) = f(x) = -4 sin(Tx) + 3 sin(27x), for 0 < x < 5.

To solve this problem, perform the following steps:

1. Assume a solution in the form u(x, t) = X(x)T(t).
2. Substitute this solution into the PDE and separate the variables.
3. Solve the resulting ordinary differential equations (ODEs) for X(x) and T(t) subject to the given boundary conditions.
4. Obtain the general solution by summing the product of the separated solutions X_n(x)T_n(t) with appropriate coefficients.
5. Determine the coefficients by applying the initial condition and using Fourier series representation.

Since the problem is well-posed, a unique solution exists.

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The null hypothesis has been true but the sample information has resulted in the rejection, when the Type I error has been made

The null hypothesis is that two possibilities are the same. The null hypothesis is that the observed difference is due to chance alone.

A type I error occurs if an investigator rejects a null hypothesis that is actually true in the population.
Hence, the null hypothesis has been true but the sample information has resulted in the rejection, when the Type I error has been made

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Answer:

b and d

Step-by-step explanation:

To solve the inequality, we can square both sides:

√x < 12

(√x)^2 < 12^2

x < 144

Therefore, any value of x that is less than 144 is a solution to the inequality.

Checking each option:

A. -144 is not a solution because the square root of a negative number is not a real number.

B. 100 is a solution because √100 = 10 < 12.

C. 144 is not a solution because the inequality is strict, meaning that x must be less than 144.

D. 4 is a solution because √4 = 2 < 12.

E. 148 is not a solution because 148 is greater than 144.

F. 32 is a solution because √32 < 12.

Therefore, the solutions are B and D.

Answer: B, D

Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

The characteristics of the correlation coefficient are A. It must be between -1 and 1. C. If the correlation is positive, the slope of the regression line is also positive. E. The correlation coefficient tells you how strong the residuals are.

The correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. Therefore, option A is correct.

Regarding option B, the correlation coefficient does not indicate the percentage of points that lie on the regression line. Instead, it measures the overall strength and direction of the relationship between the variables.

Option C is correct because if the correlation is positive, it means that as one variable increases, the other variable tends to increase as well. This positive relationship is reflected in the positive slope of the regression line.

Option D is incorrect because the correlation coefficient can be positive, negative, or zero, depending on the nature of the relationship between the variables.

Option E is correct. The correlation coefficient provides information about the strength of the relationship between the variables, which can be used to assess the strength of the residuals or the deviations from the regression line.

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Tree M most closely reflects how the three species of  the spiny back are related to one another.

The branches of the tree, which are marked with the species names, demonstrate that the three species are all closely related, but still have distinct differences between them. For example, Species 1 and 2 share a relatively recent common ancestor, while Species 3 has a much more distant one. The species are represented as separate branches of the tree to show the different pathways of evolution that each species has taken.

In conclusion, Tree M most accurately reflects the evolutionary history of the three species of the spiny back. It shows that while they are all related, they still have distinct differences between them.

The complete question is:

A single species of fish, the three-species  spiny back, once inhabited a large lake. At some point in the lake's history, lava flowed from a nearby volcano into the lake cutting it into three completely isolated mini-lakes. Despite the heat from the lava, a few individuals from the original population of spiny back survive in each mini-lake. Three million years later, a researcher finds that each mini-lake is inhabited by its own species of spiny back. Which of the following figures MOST closely reflects how the three species of spiny back are related to one another?

A.) tree H B.) tree L C.) tree M D.) tree K.

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Answer:

The answer would be 71 because x = 9 so y = 71

Answer:

20x + 12y

Step-by-step explanation:

4 times 5x = 20x

4 times 3y= 12y

Step-by-step explanation:

I am going to assume that the equivalent expression is fully simplified.

To simplify this expression, we use the distributive method.

Using this method we get:

4·(5x+3y) = 4·5x+4·3y

Now that we have the terms seperated, simplify each of them:

4·5x + 4·3y = 20x + 12y

Our expression is now fully simplified so our answer is:

20x + 12y

Hours taken by Bob and Bill if they work together is 3 1/13.

Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.

We have to find the time taken by both to do the work if done together.

Time ratio of Bob and Bill = 5: 8

Efficiency of Bob and Bill = 8: 5

Total amount of work done = 5× 8 = 8× 5 = 40

The total efficiency of Bob and Bill = 13

Hours took by both bob and bill to do the work if done together = 40/13

                                                                                                              = 3 \(\frac{1}{13}\)

Therefore the work done together is 3 \(\frac{1}{13}\) hours.

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Answer:

12.60.

Step-by-step explanation:

12.00 × 5%=.6

,6 + 12.00= 12.60

Answer:

A

Step-by-step explanation:

Because the 10 is bigger then the 4 so when you do the math (y) will equal the answer of A which its  14

Answer:

The answer is y=10+4x

Step-by-step explanation:

so because x is represented by hours you dont know how many hours someone rents the bike so x and ten dollars is a set amount so it would stand alone.

Answer:

Not a function

Step-by-step explanation:

For an equation to be a function, there should be only one y-coordinate per x-coordinate. Since this relation has both (-1,9) and (-1,4), this is not a function.

Answer:not a function

Step-by-step explanation:

because when you put the points on the coordinate plane your shape will come out as a v shaped object. In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers

To find the rate at which the diameter of a sphere is changing when the volume is 4000π/3 cm3, you can use the formula for the volume of a sphere, which is given by the equation V = (4/3)πr3, where V is the volume, π is the constant approximately equal to 3.14, and r is the radius of the sphere.

You can rearrange this formula to solve for the radius of the sphere:

r = (3V/(4π))^(1/3)

Plugging in the known values, you get:

r = (3(4000π/3)/(4π))^(1/3)

= (4000/4)^(1/3)

= 100^(1/3)

= 10

The diameter of the sphere is twice the radius, so the diameter is 2r = 2 * 10 = 20 cm.

To find the rate at which the diameter is changing, you can use the formula for the rate of change of a function, which is given by the equation rate of change = (change in y)/(change in x). In this case, the change in y is the change in the diameter of the sphere and the change in x is the change in the volume.

Since the volume is increasing at a rate of 50π cm3/min and the diameter is changing at the same time, you can use the formula to solve for the rate of change of the diameter:

rate of change = (change in y)/(change in x)

= (change in diameter)/(50π cm3/min)

To find the change in the diameter, you would need to know the initial and final diameters of the sphere. Without this information, it is not possible to determine the rate of change of the diameter.

The value of the line integral is approximately -4.3 when rounded to one decimal place.

To evaluate the line integral \(\int\limits_c(y-x) dx + (xy) dy\) along the line segment from (3,4) to (2,1), we need to parameterize the curve and then substitute the parameterization into the integrand. One possible parameterization is:

r(t) = (3-t, 4-3t), for 0 ≤ t ≤ 1

The corresponding differentials are:

dx = -dt

dy = -3dt

Substituting the parameterization and differentials into the integrand, we get:

(y-x) dx + (xy) dy = (4-3t - (3-t))(-dt) + (3-t)(4-3t)(-3dt)

= -7dt + 9t² dt

Integrating with respect to t from 0 to 1, we get:

\(\int\limits_c(y-x) dx + (xy) dy\)

= \(\int\limits_c(-7 + 9t^2)\) dt

= \([-7t + 3t^{3/3}]_0^1\)

= -4.3

Rounding to one decimal place, the line integral evaluates to -4.3.

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Step-by-step explanation:

2p - 12 = 8p - 12

Bringing like terms on one side

-12 + 12 = 8p - 2p

0 = 6p

0 - 6 = p

-6 = p

Answer:

a= (Z + 2b)/24

Step-by-step explanation:

given:

Z = 24a - 2b

to solve for a, we will try to move "a" to one side of the equation and all other terms to the other side:

Z = 24a - 2b    (add 2b to both sides)

Z + 2b = 24a -2b +2b

Z + 2b = 24a  (switch sides)

24a = Z + 2b (divide both sides by 24)

a/24 = (Z + 2b)/24

a= (Z + 2b)/24

True, Monte Carlo simulation is used for statistical sampling where larger number of trials are used for the precise result.

Step by Step Explanation:

Therefore, it is true to have more number of trials in Monte Carlo simulation  statistical sampling for precise result.

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Hey there! I'm happy to help!

The greatest common factor is the largest factor that both numbers contain. Let's look at the factors of these terms.

12x²: 1, 12, 2, 6, 3, 4, x, x

15x³: 1, 15, 3, 5, x, x ,x

We see that both of these numbers contain a 3 and 2 x's, so our GCF would be 3x².

Have a wonderful day!

The minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts

Let x represent the number of Pi Day T-shirts sold.

They are selling Pi Day T-shirts for $7.50 each, So to raise $500:

7.5x > 500

Dividing through by 7.5:

7.5x / 7.5 > 500 / 7.5

x > 66.7

Hence, the minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts

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Answer:

Not a function. The inverse is

\(y = \sqrt{ \frac{x + 5}{2} } \)

and

\(y = - \sqrt{ \frac{x + 5}{2} } \)

Step-by-step explanation:

Any even-degree polynomial functions that are inverted will not be a function.

\(f(x) = 2 {x}^{2} - 5\)

Let y = f(x)

\( y = 2 {x}^{2} - 5\)

To proceed the inverse, swap the x-term and y-term.

\(x = 2 {y}^{2} - 5\)

Convert into function form.

\(x + 5 = 2 {y}^{2} \\ 2 {y}^{2} = x + 5 \\ {y}^{2} = \frac{x +5 }{2} \)

The reason why inverted even-degree polynomial function cannot be a function because the inverse graph doesn't pass line test.

Thus the answer is

\(y = \sqrt{ \frac{x + 5}{2} } \\ y = - \sqrt{ \frac{x + 5}{2} } \)

A study conducted in 2004 examined the usage of cable television and radio among 10 individuals to determine if there was a significant difference in the average hours spent on each medium. Using a significance level of 0.05, statistical analysis was performed to test for a disparity between the population mean usage of cable television and radio.

The researchers collected data on the number of hours per week spent watching cable television and listening to the radio from a sample of 10 individuals. The objective was to determine if there was a significant difference in the average usage between cable television and radio, considering the increasing competition among various entertainment options.

To test for a difference between the population mean usage for cable television and radio, a statistical hypothesis test was conducted. The significance level (α) of 0.05 was chosen, which means that the results would be considered statistically significant if the probability of obtaining such extreme results by chance alone was less than 5%.

The test compared the means of the two samples, namely the average hours spent watching cable television and listening to the radio. By analyzing the data using appropriate statistical techniques, such as a two-sample t-test, the researchers determined whether the observed difference in means was statistically significant or could be attributed to random variation.

After conducting the hypothesis test, if the p-value associated with the test statistic was less than 0.05, it would indicate that there was a significant difference between the population mean usage of cable television and radio. Conversely, if the p-value was greater than 0.05, there would be insufficient evidence to conclude a significant disparity.

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Answer:

Below

Step-by-step explanation:

To find the slope of the line you divide the difference in y values of the points by the difference of the corresponding x values).

So here the slope =  (4-2) / (8-2}

=  2/6 = 1/3.

The student found it to be 3, so he could have divided the other way,

(8-2)/ (4 -2) =3.  In other words he divided the  difference of x-values by the y values instead of  difference of y-vales divided by x values.

To solve this problem, we can use trigonometry. Let's call the distance between the two bases "d".

From the diagram, we can see that the angle of elevation from base x is 40 degrees and the angle of elevation from base z is 28 degrees. Therefore, the two bases are 9,408 meters apart.

In order to solve it, we'll use trigonometry to find the distance between the two artillery bases, which are points X and Z in your problem. Let's follow these steps:

1. First, we need to create a right triangle with the given information. Let's say point X is A, point Z is B, and point Y (airplane) is C. Now, we have triangle ABC with right angles at A and B.

2. We are given the distance between point B (base at Z) and point C (airplane) is 3,294 meters. Let's call this distance BC. We also have the angles of elevation from point A and B to the airplane (point C). Let's call the angle of elevation from point A as ∠A and from point B as ∠B.

3. To find the distance between the two bases (points A and Z), we need to find the length of side AB in triangle ABC. To do this, we can use the tangent function, which relates the angle in a right triangle to the ratio of the opposite side and the adjacent side. In this case, we can write:

  tan(∠A) = BC / AB

  tan(∠B) = BC / (AC - AB)

Using trigonometry, we can set up the following equations:

tan(40) = h / (d/2)

tan(28) = h / ((d/2) + 3294)

4. Now, we have two equations with two unknowns (AB and AC). We can solve these equations simultaneously to find the distance AB between the two bases.

Solving for h in both equations, we get:

h = (d/2) * tan(40)

h = ((d/2) + 3294) * tan(28)

5. Using the given values of angles ∠A and ∠B, and BC = 3,294 meters, we can substitute them into the equations from step 3 and solve for AB (distance between bases X and Z).

Since both equations are equal to h, we can set them equal to each other:

(d/2) * tan(40) = ((d/2) + 3294) * tan(28)

Expanding and simplifying, we get:

0.839 * d - 1833.84 = 1.191 * d

Solving for d, we get:

d = 9408 meters

After following these steps and solving the system of equations, you will find the distance between the two bases (AB) in meters.

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